transmission_analysis
Brandi Pessman
2023-12-06
Descriptives
Sample Size
## # A tibble: 6 × 3
## # Groups: Site, treatment [6]
## Site treatment n
## <chr> <chr> <dbl>
## 1 Isolated Loud 10
## 2 Isolated Quiet 11
## 3 Rural Loud 15
## 4 Rural Quiet 15
## 5 Urban Loud 15
## 6 Urban Quiet 15Age and Condition
##
## Shapiro-Wilk normality test
##
## data: rank(spiders2$trial_age)
## W = 0.94982, p-value = 0.01528## Anova Table (Type II tests)
##
## Response: log(trial_age)
## Sum Sq Df F value Pr(>F)
## Site 0.0127 1 0.2141 0.6453
## treatment 0.0693 1 1.1662 0.2848
## Site:treatment 0.0026 1 0.0443 0.8341
## Residuals 3.3285 56## Analysis of Deviance Table (Type II tests)
##
## Response: trial_age
## LR Chisq Df Pr(>Chisq)
## Site 0.09268 1 0.7608
## treatment 1.19461 1 0.2744
## Site:treatment 0.05266 1 0.8185##
## Shapiro-Wilk normality test
##
## data: spiders2$condition
## W = 0.96166, p-value = 0.05675## Anova Table (Type II tests)
##
## Response: condition
## Sum Sq Df F value Pr(>F)
## Site 0.01352 1 0.5974 0.4428
## treatment 0.01918 1 0.8471 0.3613
## Site:treatment 0.00471 1 0.2081 0.6500
## Residuals 1.26758 56Ambient Before vs. After
Close vs Far Overall
Field Noise and Playback
noise_sum <- noise %>%
group_by(Site, Low_Freq) %>%
summarize(mean_leq = mean(Leq),
se_leq = plotrix::std.error(Leq)) %>%
mutate(Site = factor(Site),
Site = fct_recode(Site, "Urban" = "campus", "Rural" = "popes"),
Site = fct_relevel(Site, "Rural", "Urban"))
noise_sum %>%
filter(! Low_Freq < 20) %>%
ggplot() +
annotate(geom = "rect", ymin = -95, ymax = -13, xmin = range_min, xmax = range_max, fill = "grey90") +
geom_vline(xintercept = range_max, linetype = "dashed", color = "#d95f02") +
geom_vline(xintercept = range_min, linetype = "dashed", color = "#1b9e77") +
geom_line(aes(x = Low_Freq, y = mean_leq, color = Site), size = 1) +
geom_ribbon(aes(x = Low_Freq, ymin = mean_leq - se_leq, ymax = mean_leq + se_leq, fill = Site), alpha = 0.5) +
xlab("Frequency (10 Hz Bins)") +
ylab("Amplitude (Leq, dB)\nQuieter <------------> Louder") +
scale_color_manual("Collection Site", values = c("#1b9e77", "#d95f02")) +
scale_fill_manual("Collection Site", values = c("#1b9e77", "#d95f02")) +
scale_y_continuous(limits = c(-95, -13), breaks = c(-90, -75, -60, -45, -30, -15), expand = c(0,0)) +
#scale_x_continuous(expand = c(0,0)) +
theme_classic() +
theme(axis.text = element_text(size = 14, color = "black", family = "sans"),
axis.title = element_text(size = 14, color = "black", family = "sans"),
legend.text = element_text(size = 14, color = "black", family = "sans"),
legend.title = element_text(size = 14, color = "black", family = "sans"),
legend.position = "top")## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
noise_sum_urban <- noise_sum %>%
filter(Site == "Urban",
! Low_Freq < 20)
urban_dY <- diff(noise_sum_urban$mean_leq)/diff(noise_sum_urban$Low_Freq)
urban_dX <- rowMeans(embed(noise_sum_urban$Low_Freq,2))
derivativeData_u <- data.frame(X = urban_dX, Y = urban_dY, type = "Derivative", Site = "Urban")
noise_sum_rural <- noise_sum %>%
filter(Site == "Rural",
! Low_Freq < 20)
rural_dY <- diff(noise_sum_rural$mean_leq)/diff(noise_sum_rural$Low_Freq)
rural_dX <- rowMeans(embed(noise_sum_rural$Low_Freq,2))
derivativeData_r <- data.frame(X = rural_dX, Y = rural_dY, type = "Derivative", Site = "Rural")
derivativeData <- rbind(derivativeData_u, derivativeData_r)
derivativeData2 <- derivativeData %>%
pivot_wider(names_from = "Site", values_from = "Y") %>%
mutate(diff = round(Urban-Rural, 2))
ggplot(derivativeData, aes(X,Y, color = Site)) +
geom_line(size = 1) +
geom_hline(yintercept = -0.0116700000, linetype = "dashed") +
geom_hline(yintercept = -0.0129166667, linetype = "dashed") +
geom_vline(xintercept = range_min, linetype = "dashed", color = "#1b9e77") +
geom_vline(xintercept = range_max, linetype = "dashed", color = "#d95f02") +
xlab("Frequency (10 Hz Bins)") +
ylab("First Derivative of Amplitude/Frequency") +
scale_color_manual("Collection Site", values = c("#1b9e77", "#d95f02")) +
scale_y_continuous(limits = c(-0.2, 0.2)) +
theme_classic() +
theme(axis.text = element_text(size = 14, color = "black", family = "sans"),
axis.title = element_text(size = 14, color = "black", family = "sans"),
legend.text = element_text(size = 14, color = "black", family = "sans"),
legend.title = element_text(size = 14, color = "black", family = "sans"),
legend.position = "top")
#rural_dY2 <- diff(derivativeData_r$Y)/diff(derivativeData_r$X)
#rural_dX2 <- rowMeans(embed(derivativeData_r$X,2))
#derivativeData_r2 <- data.frame(X2 = rural_dX2, Y2 = rural_dY2, type = "Derivative2", Site = "Rural")
#urban_dY2 <- diff(derivativeData_u$Y)/diff(derivativeData_u$X)
#urban_dX2 <- rowMeans(embed(derivativeData_u$X,2))
#derivativeData_u2 <- data.frame(X2 = urban_dX2, Y2 = urban_dY2, type = "Derivative2", Site = "Urban")
#derivativeData2 <- rbind(derivativeData_u2, derivativeData_r2)
#ggplot(derivativeData2, aes(X2,Y2, color = Site)) +
# geom_line(size = 1) +
# geom_hline(yintercept = 0.000095, linetype = "dashed") +
# geom_hline(yintercept = 0, linetype = "dashed") +
# geom_vline(xintercept = 380, linetype = "dashed", color = #"#1b9e77") +
# geom_vline(xintercept = 740, linetype = "dashed", color = #"#d95f02") +
# xlab("Frequency (10 Hz Bins)") +
# ylab("Second Derivative of Amplitude/Frequency") +
# scale_color_manual("Collection Site", values = c("#1b9e77", #"#d95f02")) +
# theme_classic() +
# scale_y_continuous(limits = c(-0.0010, 0.0010)) +
# theme(axis.text = element_text(size = 14, color = "black", #family = "sans"),
# axis.title = element_text(size = 14, color = "black", #family = "sans"),
# legend.text = element_text(size = 14, color = #"black", family = "sans"),
# legend.title = element_text(size = 14, color = #"black", family = "sans"),
# legend.position = "top")
playback <- read.csv("data/playback.csv")
playback %>%
ggplot() +
geom_vline(xintercept = range_min) +
geom_vline(xintercept = range_max) +
geom_line(aes(x = frequency, y = Leq, group = interaction(tub, treatment), color = treatment)) +
xlab("Frequency (10 Hz Bins)") +
ylab("Corrected Amplitude (Leq, dB)") +
scale_color_manual(values = c("#d95f02", "#1b9e77")) +
#scale_y_continuous(limits = c(0, 40), breaks = c(seq(0, 40, 5))) +
theme_classic() +
theme(axis.text = element_text(size = 12, color = "black"),
axis.title = element_text(size = 12, color = "black"),
legend.text = element_text(size = 12, color = "black"),
legend.title = element_text(size = 12, color = "black"),
legend.position = "top")
playback %>%
filter(! frequency < 20) %>%
group_by(treatment, frequency) %>%
summarize(mean_leq = mean(leq_test),
se_leq = plotrix::std.error(leq_test)) %>%
ggplot() +
annotate(geom = "rect", ymin = -95, ymax = -13, xmin = range_min, xmax = range_max, fill = "grey90") +
geom_vline(xintercept = range_min, linetype = "dashed", color = "#1b9e77") +
geom_vline(xintercept = range_max, linetype = "dashed", color = "#d95f02") +
geom_line(aes(x = frequency, y = mean_leq, color = treatment)) +
geom_ribbon(aes(x = frequency, ymin = mean_leq - se_leq, ymax = mean_leq + se_leq, fill = treatment), alpha = 0.5) +
xlab("Frequency (10 Hz Bins)") +
ylab("Amplitude (Leq, dB)\nQuieter <------------> Louder") +
scale_color_manual("Treatment", values = c("#d95f02", "#1b9e77"),
labels = c("Loud", "Quiet")) +
scale_fill_manual("Treatment", values = c("#d95f02", "#1b9e77"),
labels = c("Loud", "Quiet")) +
scale_y_continuous(limits = c(-95, -13), breaks = c(-90, -75, -60, -45, -30, -15), expand = c(0,0)) +
theme_classic() +
theme(axis.text = element_text(size = 14, color = "black", family = "sans"),
axis.title = element_text(size = 14, color = "black", family = "sans"),
legend.text = element_text(size = 14, color = "black", family = "sans"),
legend.title = element_text(size = 14, color = "black", family = "sans"),
legend.position = "top",
#legend.key.size = unit(1, "cm")
)
Stimulus
Research Questions
Vibration Transmissiion
Do webs built by urban and rural spiders under different vibratory conditions differ in the frequency transmission properties?
##
## Shapiro-Wilk normality test
##
## data: close_1000$mean_leq
## W = 0.99233, p-value = 0.7515## Analysis of Deviance Table (Type II Wald chisquare tests)
##
## Response: mean_leq
## Chisq Df Pr(>Chisq)
## Site 0.0000 1 1.00000
## treatment 0.0000 1 1.00000
## Freq 48.9885 1 0.000000000002575 ***
## Site:treatment 0.0000 1 1.00000
## Site:Freq 0.9538 1 0.32876
## treatment:Freq 1.2335 1 0.26673
## Site:treatment:Freq 5.8919 1 0.01521 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Site = Rural, treatment = Quiet:
## contrast estimate SE df t.ratio p.value
## (0-1000) - (1000-2000) 2.577 0.774 56 3.330 0.0015
##
## Site = Urban, treatment = Quiet:
## contrast estimate SE df t.ratio p.value
## (0-1000) - (1000-2000) 3.701 0.774 56 4.780 <.0001
##
## Site = Rural, treatment = Loud:
## contrast estimate SE df t.ratio p.value
## (0-1000) - (1000-2000) 3.597 0.774 56 4.646 <.0001
##
## Site = Urban, treatment = Loud:
## contrast estimate SE df t.ratio p.value
## (0-1000) - (1000-2000) 0.962 0.774 56 1.242 0.2193
##
## Degrees-of-freedom method: kenward-roger##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Freq
## Kruskal-Wallis chi-squared = 12.873, df = 1, p-value = 0.0003334##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Freq
## Kruskal-Wallis chi-squared = 8.551, df = 1, p-value = 0.003453##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Freq
## Kruskal-Wallis chi-squared = 1.8172, df = 1, p-value = 0.1776##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Freq
## Kruskal-Wallis chi-squared = 16.355, df = 1, p-value = 0.00005252
## Warning in predict.merMod(model_close_1000, newdata = nd, se.fit = TRUE, :
## unused arguments ignored
##
## Shapiro-Wilk normality test
##
## data: far_1000$mean_leq
## W = 0.95461, p-value = 0.0004788## Analysis of Deviance Table (Type II Wald chisquare tests)
##
## Response: mean_leq
## Chisq Df Pr(>Chisq)
## Site 0.0000 1 1.0000
## treatment 0.0000 1 1.0000
## Freq 17.5437 1 0.00002808 ***
## Site:treatment 0.0000 1 1.0000
## Site:Freq 0.0019 1 0.9651
## treatment:Freq 0.0501 1 0.8230
## Site:treatment:Freq 0.8913 1 0.3451
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Site = Rural, treatment = Loud:
## contrast estimate SE df t.ratio p.value
## (0-1000) - (1000-2000) -0.955 0.623 56 -1.532 0.1311
##
## Site = Urban, treatment = Loud:
## contrast estimate SE df t.ratio p.value
## (0-1000) - (1000-2000) -1.516 0.623 56 -2.433 0.0182
##
## Site = Rural, treatment = Quiet:
## contrast estimate SE df t.ratio p.value
## (0-1000) - (1000-2000) -1.683 0.623 56 -2.700 0.0092
##
## Site = Urban, treatment = Quiet:
## contrast estimate SE df t.ratio p.value
## (0-1000) - (1000-2000) -1.067 0.623 56 -1.712 0.0924
##
## Degrees-of-freedom method: kenward-roger##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Freq
## Kruskal-Wallis chi-squared = 0.95011, df = 1, p-value = 0.3297##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Freq
## Kruskal-Wallis chi-squared = 4.2155, df = 1, p-value = 0.04006##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Freq
## Kruskal-Wallis chi-squared = 5.8877, df = 1, p-value = 0.01525##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Freq
## Kruskal-Wallis chi-squared = 5.6882, df = 1, p-value = 0.01708
## Warning in predict.merMod(model_far_1000, newdata = nd, se.fit = TRUE, re.form =
## NA, : unused arguments ignored
Distance | Residual DF | Collection Site | Treatment | 0-1000 Hz | 1000-2000 Hz | Test Statistic | P-Value |
|---|---|---|---|---|---|---|---|
Closea | 110 | Rural | Quiet | 1.29 (0.55) | -1.29 (0.55) | 3.330 | 0.002 ** |
Urban | Quiet | 1.85 (0.42) | -1.85 (0.42) | 4.780 | < 0.001 *** | ||
Rural | Loud | 1.80 (0.51) | -1.80 (0.51) | 4.646 | < 0.001 *** | ||
Urban | Loud | 0.48 (0.68) | -0.48 (0.68) | 1.242 | 0.219 | ||
Farb | 28 | Rural | Quiet | -0.84 (0.56) | 0.84 (0.56) | 4.216 | 0.040 * |
Urban | Quiet | -0.53 (0.27) | 0.53 (0.27) | 5.688 | 0.017 * | ||
Rural | Loud | -0.48 (0.41) | 0.48 (0.41) | 0.950 | 0.330 | ||
Urban | Loud | -0.76 (0.48) | 0.76 (0.48) | 5.888 | 0.015 * | ||
aResults of pairwise comparison following a linear mixed effects model with t-ratio as the test statistic. | |||||||
bResults of individual Kruskal-Wallis tests following subsetting by collection site and treatment with a chi-squared value as the test statistic. | |||||||
##
## Shapiro-Wilk normality test
##
## data: close_noise$mean_leq
## W = 0.98648, p-value = 0.7464## Anova Table (Type II tests)
##
## Response: mean_leq
## Sum Sq Df F value Pr(>F)
## Site 16.14 1 0.7836 0.37983
## treatment 2.34 1 0.1136 0.73732
## Site:treatment 79.07 1 3.8389 0.05506 .
## Residuals 1153.40 56
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## treatment = Quiet:
## contrast estimate SE df t.ratio p.value
## Rural - Urban -1.26 1.66 56 -0.760 0.4507
##
## treatment = Loud:
## contrast estimate SE df t.ratio p.value
## Rural - Urban 3.33 1.66 56 2.011 0.0491## Site = Rural:
## contrast estimate SE df t.ratio p.value
## Quiet - Loud -1.90 1.66 56 -1.147 0.2562
##
## Site = Urban:
## contrast estimate SE df t.ratio p.value
## Quiet - Loud 2.69 1.66 56 1.624 0.1100
##
## Shapiro-Wilk normality test
##
## data: far_noise$mean_leq
## W = 0.9366, p-value = 0.003828##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Site
## Kruskal-Wallis chi-squared = 4.2155, df = 1, p-value = 0.04006##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by Site
## Kruskal-Wallis chi-squared = 1.3974, df = 1, p-value = 0.2372##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by treatment
## Kruskal-Wallis chi-squared = 0.41333, df = 1, p-value = 0.5203##
## Kruskal-Wallis rank sum test
##
## data: mean_leq by treatment
## Kruskal-Wallis chi-squared = 2.6843, df = 1, p-value = 0.1013
Isolated
Frequency Response
Do spiders shift their response to frequencies based on experience with different vibratory conditions?
2022 - Deciding to pool rural but not urban (campus only)
## # A tibble: 4 × 2
## # Groups: Location [4]
## Location n
## <chr> <int>
## 1 Campus 230
## 2 Corman 120
## 3 Herman 200
## 4 Pope 120## # A tibble: 2 × 2
## # Groups: Site [2]
## Site n
## <chr> <int>
## 1 Rural 320
## 2 Urban 350## # A tibble: 4 × 2
## # Groups: Location [4]
## Location n
## <chr> <int>
## 1 Campus 190
## 2 Corman 110
## 3 Herman 200
## 4 Pope 100## # A tibble: 2 × 2
## # Groups: Site [2]
## Site n
## <chr> <int>
## 1 Rural 300
## 2 Urban 300
Frequency Response
## # A tibble: 6 × 3
## # Groups: Group, Site [6]
## Group Site n
## <fct> <chr> <int>
## 1 2022 Rural 320
## 2 2022 Urban 230
## 3 2023_Quiet Rural 120
## 4 2023_Quiet Urban 140
## 5 2023_Loud Rural 100
## 6 2023_Loud Urban 130
## # A tibble: 6 × 3
## # Groups: Group, Site [6]
## Group Site n
## <fct> <chr> <int>
## 1 2022 Rural 300
## 2 2022 Urban 190
## 3 2023_Quiet Rural 70
## 4 2023_Quiet Urban 120
## 5 2023_Loud Rural 60
## 6 2023_Loud Urban 100
## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
Isolated Frequency Responses
## # A tibble: 4 × 3
## # Groups: before_after, treatment [4]
## before_after treatment n
## <chr> <chr> <int>
## 1 After Loud 60
## 2 After Quiet 40
## 3 Before Loud 100
## 4 Before Quiet 100
## # A tibble: 4 × 3
## # Groups: before_after, treatment [4]
## before_after treatment n
## <chr> <chr> <int>
## 1 After Loud 50
## 2 After Quiet 30
## 3 Before Loud 80
## 4 Before Quiet 90
Silk Mass
##
## Shapiro-Wilk normality test
##
## data: log(silk$dry_microg_body_mg)
## W = 0.95149, p-value = 0.01831## Anova Table (Type II tests)
##
## Response: log(dry_microg_body_mg)
## Sum Sq Df F value Pr(>F)
## Site 1.564 1 2.0345 0.1593
## treatment 0.042 1 0.0541 0.8169
## Site:treatment 1.151 1 1.4971 0.2262
## Residuals 43.041 56## Site = Rural:
## contrast estimate SE df t.ratio p.value
## Quiet - Loud -0.224 0.32 56 -0.701 0.4864
##
## Site = Urban:
## contrast estimate SE df t.ratio p.value
## Quiet - Loud 0.330 0.32 56 1.030 0.3076
##
## Results are given on the log (not the response) scale.## treatment = Quiet:
## contrast estimate SE df t.ratio p.value
## Rural - Urban 0.0459 0.32 56 0.143 0.8865
##
## treatment = Loud:
## contrast estimate SE df t.ratio p.value
## Rural - Urban 0.5998 0.32 56 1.874 0.0662
##
## Results are given on the log (not the response) scale.##
## Kruskal-Wallis rank sum test
##
## data: dry_microg_body_mg by Site
## Kruskal-Wallis chi-squared = 3.4069, df = 1, p-value = 0.06493##
## Kruskal-Wallis rank sum test
##
## data: dry_microg_body_mg by Site
## Kruskal-Wallis chi-squared = 0.021075, df = 1, p-value = 0.8846
##
## Shapiro-Wilk normality test
##
## data: log(silk$moisture_per)
## W = 0.95805, p-value = 0.03781## Anova Table (Type II tests)
##
## Response: log(moisture_per)
## Sum Sq Df F value Pr(>F)
## Site 0.5465 1 1.0878 0.30143
## treatment 1.7789 1 3.5411 0.06507 .
## Site:treatment 0.9967 1 1.9840 0.16450
## Residuals 28.1323 56
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Kruskal-Wallis rank sum test
##
## data: moisture_per by treatment
## Kruskal-Wallis chi-squared = 0.096774, df = 1, p-value = 0.7557##
## Kruskal-Wallis rank sum test
##
## data: moisture_per by treatment
## Kruskal-Wallis chi-squared = 3.8817, df = 1, p-value = 0.04881## Analysis of Deviance Table (Type II tests)
##
## Response: moisture_per
## Df Chisq Pr(>Chisq)
## Site 1 0.6103 0.43468
## treatment 1 3.0969 0.07844 .
## Site:treatment 1 2.1328 0.14418
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Site = Rural:
## contrast estimate SE df z.ratio p.value
## Quiet - Loud -0.1009 0.0441 Inf -2.290 0.0220
##
## Site = Urban:
## contrast estimate SE df z.ratio p.value
## Quiet - Loud -0.0119 0.0466 Inf -0.256 0.7978## treatment = Quiet:
## contrast estimate SE df z.ratio p.value
## Rural - Urban -0.0684 0.0426 Inf -1.605 0.1085
##
## treatment = Loud:
## contrast estimate SE df z.ratio p.value
## Rural - Urban 0.0206 0.0480 Inf 0.429 0.6681
Dependent Variable | Test | Residual DF | Independent Variable | Test Statistic | P-Value |
|---|---|---|---|---|---|
Dry Silk Mass (µg) per Body Mass (mg) | ANOVAa | 56 | Collection Site | 2.035 | 0.159 |
Treatment | 0.054 | 0.817 | |||
Collection Site x Treatment | 1.497 | 0.226 | |||
Prop. Silk Moisture | Beta Regression b | 56 | Collection Site | 0.610 | 0.435 |
Treatment | 3.097 | 0.078 . | |||
Collection Site x Treatment | 2.133 | 0.144 | |||
aTest statistic: F-value | |||||
bTest statistic: Chi-squared value | |||||
## Warning in read.table(file = file, header = header, sep = sep, quote = quote, :
## incomplete final line found by readTableHeader on 'tables/multicomp_silk.csv'Dependent Variable | Residual DF | Comparison | Level | Test Statistic | P-Value |
|---|---|---|---|---|---|
Dry Silk Mass (µg) per Body Mass (mg) | 56 | Collection Site | Quiet | 0.143a | 0.887 |
Loud | 1.874a | 0.066 . | |||
Prop. Silk Moisture | 56 | Treatment | Rural | -2.290b | 0.022 * |
Urban | -0.256b | 0.798 | |||
aTest statistic: t-ratio | |||||
bTest statistic: z-ratio | |||||